Brush each chop with 1 teaspoon of the mustard; generously sprinkle all over with coarsely ground black pepper.
In a large skillet, heat 2 tablespoons of the olive oil until shimmering.
Add the pork chops and cook over moderate heat, turning once, until golden, about 6 minutes.
Transfer the chops to a baking sheet and roast for 12 minutes, until cooked through; keep warm.
Meanwhile, pour off the fat from the skillet.
Add 1/4 cup of water and cook over high heat for 1 minute, scraping up any browned bits from the bottom of the pan.
Pour the pan juices into a cup and wipe out the skillet.
Heat 2 tablespoons of the olive oil in the skillet.
Add all but 1 tablespoon of the shallots and cook over moderately high heat until softened, 3 minutes.
Add the vinegar and cook until nearly evaporated, about 30 seconds.
Add the wine and cook until nearly evaporated, about 2 minutes.
Add the cream and cook over moderately high heat until slightly reduced, about 2 minutes.
Add the remaining 4 teaspoons of mustard, the reserved pan juices and half of the parsley.
Season the sauce with salt and finely ground black pepper; keep warm.
Heat the remaining 2 tablespoons of olive oil in another large skillet.
Add the sugar snaps, mushrooms, scallions and the reserved 1 tablespoon of shallots and cook over moderately high heat until the sugar snaps are crisp-tender and the mushrooms are tender and lightly browned, about 5 minutes.
Stir in the peas and the remaining parsley and season with salt and finely ground pepper.
Pour the cream sauce onto plates and top with the pork chops.